In the common practice of shaving hair, a user removes a small portion of the outer layers of skin along with the hair that is cut resulting in a smoother and shinier skin appearance. It has been known in the art to exfoliate skin with abrasive material comprising particulates, e.g. sand, ground shells, seeds, kernels, beads, polymeric particles, etc., prior to or while shaving as detailed in US Patent Publications 2007/0227006 A1 and 2004/0181943 A1 and even as far back as the issuance of U.S. Pat. No. 3,939,560. In other approaches, shavers have been introduced to shaving implements that do not include typical razor blades. For instance, U.S. Pat. No. 7,007,393 B2, issued to Guimont on Mar. 7, 2006, discloses a microreplicated shaving elements that define cutting edges spaced away from a substrate's surface in combination with a plurality of guard elements attached to and extending outwardly from the substrate. Similarly, US Patent Publication 2006/003060 A1 filed in the name of Nicolosi et al. and published on Feb. 16, 2006, discloses a microprismatic shaving element for abrasively removing hair where it includes a substrate having a plurality of contiguous raised portions projecting outwardly therefrom. When this shaving element is used during a shaving operation, the contiguous raised portions defining the abrasive surface engage the hair protruding from a user's skin and abrade portions of the hair away, leaving a frayed hair end that is tactilely smooth and gives a feel of a close shave. Another reference, US Patent Publication 2005/0235495 A1 relates to a wet shaving system that includes blades mounted on a housing that further includes an exfoliation member and a drive mechanism that provides repeating movement to the exfoliating member. Additionally, US Patent Publication 2002/0177858 A1 relates to an apparatus involving a substrate with a plurality of microelements affixed to the substrate for scraping skin cells from the surface of the skin and methods of using such an apparatus. None of these references, however, capitalizes on the benefit of combining a plurality of razor blades with an abrasion material of the type Applicant describes herein in an integrated wet shaving razor. As a consequence, Applicant seeks to provide a wet shaving razor that not only provides a feeling of a “close” shave but rather an actually closer shave than would be achieved without razor blades or without incorporating an abrasive material as described herein.